NIMCET 2007 — Computer PYQ

Step 1: Understand the Logical Operator

The expression $p\to q$ represents a conditional statement (also known as an implication), which translates to "If $p$, then $q$".

• $p$ is called the hypothesis or antecedent.

• $q$ is called the conclusion or consequent.

Step 2: Review the Truth Table for Implication

A conditional statement $p\to q$ is only considered False when the premise $p$ is True, but the conclusion $q$ turns out to be False. In all other scenarios, the statement evaluates to True.

Here is the standard truth table for $p\to q$:

Step 3: Apply the Given Conditions

The problem specifically states that $p$ is false.

Looking at the truth table, whenever the antecedent $p$ is False, the conditional implication $p\to q$ automatically results in True, completely independent of whether $q$ is true or false. This mathematical concept is often referred to as being vacuously true.

$$\text{If }p=\text{False}⟹(p\to q)=\text{True}$$

Conclusion

The truth value of $p\to q$ when $p$ is false is True.

Correct Answer: (b) True